Universal logic is the field of logic that is concerned with giving an account of what features are common to all logical structures. Universal logic aims to be to logic what universal algebra is to algebra; currently there is no universally accepted notion of logic (or logical system). Several frameworks have been proposed.
The term 'universal logic' was introduced in the 1990s by Swiss logician Jean-Yves Béziau, but the field has arguably existed for many decades. Some of the works of Alfred Tarski in the early twentieth century, for example, can be regarded as fundamental contributions to universal logic.
Three model-theoretic directions for universal logic have been explored to some depth: abstract model theory axiomatized by Jon Barwise, a topological / categorical approach based on sketches (sometimes called categorical model theory), and yet another categorical approach based on Goguen and Burstall's notion of institution.
The First World Congress and School on Universal Logic took place in Montreux, Switzerland in early 2005. Participants included Béziau, Dov Gabbay, Saul Kripke, and David Makinson. A journal dedicated to the field, Logica Universalis, with Béziau as editor-in-chief started to be published by Birkhäuser Basel (an imprint of Springer) in 2007. Springer also started to publish a book series on the topic, Studies in Universal Logic, with Béziau as series editor.
The term 'universal logic' has also been used by some logicians (e.g. Richard Sylvan and Ross Brady) to refer to a new type of (weak) relevant logic.
In 2012 was published an anthology of universal logic giving a new light on the subject.
Famous quotes containing the words universal and/or logic:
“Not so many years ago there there was no simpler or more intelligible notion than that of going on a journey. Travel—movement through space—provided the universal metaphor for change.... One of the subtle confusions—perhaps one of the secret terrors—of modern life is that we have lost this refuge. No longer do we move through space as we once did.”
—Daniel J. Boorstin (b. 1914)
“The logic of worldly success rests on a fallacy: the strange error that our perfection depends on the thoughts and opinions and applause of other men! A weird life it is, indeed, to be living always in somebody else’s imagination, as if that were the only place in which one could at last become real!”
—Thomas Merton (1915–1968)